Car stalling

I've got a 1993 Mustang Cobra and for the first time since buying it, I am having a problem. In the past 2 days, the car has died 3 times; always when engaging the clutch. The first time was at a stop light. The following 2 times occured while moving while shifting. Here is what is weird though: When it dies, all the power in the cabin also goes out; i.e. the radio goes dead and the clock resets to 12:00, the lights go dead. It is like the car was hit by an EMP However, when the car died at the light, it started right back up and when it was rolling, I just let the clutch out and it started so it has no problem starting again. It also started today with no problem. I didn't have much time to look at it when I got home today but I was wondering where I should start. Could a loose ground wire cause this? Starter selenoid? Bad alternator? Any ideas?

Details on the car: 73,000 original miles, only mods are headers/exhaust, new battery.

Thanks in advance for any help you guys might have to offer. I am going to start chasing down the problem tomorrow after work.

Chris